担 has two readings. First-tone dān is the verb 'to carry / undertake': 担心 (to worry), 担任 (to serve as), 承担 (to bear). Fourth-tone dàn is the noun 'a load / picul / classifier for shoulder-pole loads': 重担 (heavy burden), 担子.
memory
The action of carrying is dān (level first tone, you are still holding it up); the thing carried, the load that drops onto your shoulder, is dàn (falling fourth tone), as in 担子.
旦 supplies the sound, with a tone shift dàn to dān. In simplified 担 it replaced traditional 擔's 詹 phonetic, a major reform substitution. The 'dawn' meaning has no role; pure sound shorthand.
